Séminaires : Séminaire d'Algèbres d'Opérateurs

Equipe(s) : ao,
Responsables :Pierre Fima, François Le Maître, Romain Tessera
Email des responsables :
Salle : 1013
Adresse :Sophie Germain

Orateur(s) Marek Kaluba - Karlsruhe Institute of Technology,
Titre Aut(Fₙ) has property (T)
Horaire14:00 à 15:00
RésumeThe aim of the lecture is to show that Aut(Fₙ), the automorphism group of the free group has Kazdhan property (T). I will begin by studying the structure of Aut(Fₙ) and the action of its "Weyl group". Then I will show you how to square the group Laplacian in a form that is compatible with the action. This description can be then used to define operators Adjₙ and Opₙ and reformulate property (T) in terms of their positivity. Finally I will show to use the Weyl group to reduce property (T) for Aut(Fₙ) for any n ≥ 5 to a sum of squares problem in ℝ[Aut(F₅)] which can be effectively checked on a computer. The talk will be based on 1812.03456 by D.Kielak, P.Nowak and myself.
AdresseSophie Germain